Methods for scanning an examined object with a CT system are generally known, wherein circular scans, sequential circular scans with forward-feed motion, or spiral scans can be used. These scans are designed to record absorption data of the examined object from different angles, which are recorded with the aid of at least one X-ray source and at least one opposite-arranged detector. The collected projection data are then converted with the aid of corresponding reconstruction methods to obtain sectional or volume images through the examined object.
A so-called filtered back projection process (FBP) is used nowadays as standard method for the reconstruction of computer tomography images from X-ray CT data sets of a CT device, for which during the data acquisition an X-ray source emitting cone-shaped X rays moves along a helical path around the object to be detected and/or the volume of interest (VoI). This method functions quite well in principle but is an approximation method, meaning that mathematically precise reconstructions are not possible, thereby resulting in artifacts. Problems with the so-called cone beam artifacts occur in particular when using the FBP method because it is an approximation method. These artifacts furthermore increase along with an increase in the number of detector lines, which is particularly serious if the number of detector lines increases noticeably, for example exceeds 100, as can be the case with the newest types of detectors.
Attempts have therefore been made to develop methods, which permit a mathematically precise and stable reconstruction. The “differentiated back projection” along so-called “n lines” is one example of such an attempt. Referred to as n lines are in particular those lines which twice intersect the helical path at a distance of less than one complete rotation. The resulting back projection data correspond to the Hilbert transform of the desired image data, so that the desired image data can subsequently be computed with a following inverse Hilbert transformation. The method for a three-dimensional differentiated back projection with subsequent inverse Hilbert transformation is described in further detail in the publication by H. Schondube, K. Stierstorfer, F. Dennerlein, T. White and F. Noo: “Towards an efficient two-step Hilbert algorithm for helical cone-beam CT.” in Proc. 2007 Meeting on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine (Lindau, Germany), F. Beckman and M. Kachelriess, Edition 2007, pp 120-123, the entire contents of which are hereby incorporated herein by reference. Since this method is mathematically accurate and no artifacts can occur because of the fan geometry of the X-ray beam, it can be used to reconstruct good images even if the number of detector lines increases strongly, as described in the above.
However, this reconstruction method is restricted to the use of measuring data from the detector which are located within the so-called Tam-Danielsson window (henceforth called “TD window”) on the detector. This TD window is defined by the projection onto the detector of the X-ray source trajectory, meaning the helical path of the X-ray source. Data measured in the detector regions outside of this TD window cannot be used with the aforementioned method. However, since the conical beam from the X-ray source of standard CT systems is formed such that it hits the complete detector, meaning also the regions outside of the TD window, some amounts of the radiation dose remain unused. To be sure, it would theoretically be possible to design the X-ray source such that it can generate an X-ray beam that impinges precisely on the TD window. However, this would result in no flexibility for adjusting the pitch height of the helical curve, meaning the pitch, and would otherwise be extremely costly so that it makes more sense to use a rectangular standard detector with a traditional X-ray source.
However, it is desirable to be able to use data outside of the TD window. In contrast to data measured inside the TD window, the data measured outside of this window are redundant and are not required for a complete reconstruction. These redundant data can be used to reduce the image noise while maintaining the same image resolution.
Approximation methods can in principle be used for utilizing redundant data, wherein again the advantage of the above-described mathematically precise reconstruction is lost. The publication by J. Pack, F. Noo and R. Clackdoyle: “Cone-beam reconstruction using the back projection of locally filtered projections,” IEEE Trans. Med. Imag., Vol. 24, No. 1, pp 70-85, January 2005, describes an approach for a mathematically precise reconstruction that also allows using detector data measured outside of the TD window. However, this method is limited to realizing a differentiated back projection and a subsequent inverse Hilbert transformation for each individual voxel, wherein multiple reconstructions are respectively used for the individual voxels, which then requires an averaging of the reconstruction values of the individual voxels. This results in considerable computation expenditure for reconstructing a complete volume of interest, making this method very inefficient and unusable in everyday practice.